Uninterpreted Function
In mathematical logic, an uninterpreted function or function symbol is one that has no other property than its name and '' n-ary'' form. Function symbols are used, together with constants and variables, to form terms. The theory of uninterpreted functions is also sometimes called the free theory, because it is freely generated, and thus a free object, or the empty theory, being the theory having an empty set of sentences (in analogy to an initial algebra). Theories with a non-empty set of equations are known as equational theories. The satisfiability problem for free theories is solved by syntactic unification In logic and computer science, unification is an algorithmic process of solving equations between symbolic expressions. Depending on which expressions (also called ''terms'') are allowed to occur in an equation set (also called ''unification prob ...; algorithms for the latter are used by interpreters for various computer languages, such as Prolog. Syntactic unific ...
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